English

Relative entropy in multi-phase models of 1d elastodynamics: Convergence of a non-local to a local model

Analysis of PDEs 2014-05-12 v1

Abstract

In this paper we study a local and a non-local regularization of the system of nonlinear elastodynamics with a non-convex energy. We show that solutions of the non-local model converge to those of the local model in a certain regime. The arguments are based on the relative entropy framework and provide an example how local and non-local regularizations may compensate for non-convexity of the energy and enable the use of the relative entropy stability theory -- even if the energy is not quasi- or poly-convex.

Keywords

Cite

@article{arxiv.1405.2223,
  title  = {Relative entropy in multi-phase models of 1d elastodynamics: Convergence of a non-local to a local model},
  author = {Jan Giesselmann},
  journal= {arXiv preprint arXiv:1405.2223},
  year   = {2014}
}